A force F = (2i + 4j ) N displaces the body by s = (3j + 5k ) m in 2 sec. Power generated will be

Q: A force $ \vec{F} = (2 \hat{i} + 4 \hat{j} ) $ N displaces the body by $ \vec{s} = ( 3 \hat{j} + 5 \hat{k} ) $ m in 2 sec. Power generated will be

(a) 11 watt

(b) 6 watt

(c)22 watt

(d) 12 watt

Click to See Answer :
Ans: (b)
Sol: Power , $\displaystyle P = \vec{F}.\vec{v} $

$\displaystyle \vec{v} = \frac{\vec{s}}{t} $

$\displaystyle \vec{v} =  \frac{3}{2} \hat{j} + \frac{5}{2} \hat{k}  $

$\displaystyle P = (2 \hat{i} + 4 \hat{j} ) . (\frac{3}{2} \hat{j} + \frac{5}{2} \hat{k} ) $

P = 6 Watt